Finite Group Databasebeta

← #34079071

Subgroups — #34079071

Order 19328.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752781C211yesmaximal, characteristic
2#23752692C211yesmaximal, characteristic, complemented
3#23752539C212yesmaximal, complemented
4#23752538C212yesmaximal, complemented
5#23752532C212yesmaximal, complemented
6#23752527C212yesmaximal, complemented
7#23752255C211yesmaximal, characteristic, complemented
8#23752216C211yesmaximal, characteristic, complemented
9C2×#18012661C211yesmaximal, characteristic, complemented
10#23752178C211yesmaximal, characteristic, complemented
11#427×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C2×#14558988C2211yescharacteristic
15#18012736—21no—
16#18012727—21no—
17#18012714C2212yes—
18#18012714C2212yes—
19#18012709—22no—
20C4×Dic302—21no—
21C4×D604—21no—
22(C22⋊D151)⋊C4—22no—
23#18012697C2212yescomplemented
24C2×C4⋊Dic151C2211yescharacteristic
25C4⋊C4×D151C2212yescomplemented
26#18012672C2212yescomplemented
27#18012670C2212yescomplemented
28#18012661C2212yes—
29#18012661C2212yes—
30#18012659C2212yes—
31#18012659C2212yes—
32(C2×D151)⋊C8C2212yescomplemented
33(C2×D151)⋊C8C2212yescomplemented
34C22×C8×C151C2211yescharacteristic
35#117×C151C2211yescharacteristic
36#117×C151C2211yescharacteristic
37#107×C151C2211yescharacteristic, complemented
38#107×C151C2211yescharacteristic, complemented
39#106×C151C2211yescharacteristic, complemented
40#106×C151C2211yescharacteristic, complemented
41C23×D151—21no—
42#14559004—22no—
43#14559004—22no—
44C2×Dic302D411yescharacteristic
45C2×D604—22no—
46C2×D604—22no—
47C2×D604—21no—
48C2×D604—22no—
49C2×D604—22no—
50C2×D604D411yescharacteristic
51C2×D604C2312yes—
52C2×C22⋊D151D412yes—
53C22×Dic151—21no—
54C2×C4×D151—22no—
55C2×C4×D151C2312yes—
56#14558988—22no—
57C2×C151⋊C8C2312yes—
58C4⋊Dic151—21no—
59C4⋊Dic151C2312yes—
60Dic151⋊C4—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—22no—
64C4×Dic151—22no—
65C22×C4×C151C2311yescharacteristic
66C2×C8×C151—22no—
67C2×C8×C151C2311yescharacteristic
68C2×C8×C151C2311yescharacteristic
69C4⋊C4×C151C2311yescharacteristic
70C4⋊C4×C151C2311yescharacteristic
71C4⋊C4×C151C2311yescharacteristic
72C4⋊C4×C151C2311yescharacteristic
73C22⋊C4×C151—21no—
74C22⋊C4×C151—21no—
75C42×C151—21no—
76C42×C151—21no—
77C22×D151—22no—
78C22×D151—42no—
79C22×D151—81no—
80C22×D151—81no—
81C22×D151C2×D412yes—
82Dic302—22no—
83D604—22no—
84D604—22no—
85D604—22no—
86D604—42no—
87D604—82no—
88D604—82no—
89C22⋊D151—24no—
90C2×Dic151—22no—
91C2×Dic151—81no—
92C2×Dic151C2×D412yes—
93C4×D151—22no—
94C4×D151—22no—
95C4×D151—82no—
96C151⋊C8—22no—
97C23×C151C2×D411yescharacteristic
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151#4112yes—
104C2×C4×C151#4112yes—
105C2×C4×C151C2411yescharacteristic
106C8×C151—21no—
107C8×C151—21no—
108C22×C151—21no—
109C22×C151—21no—
110C22×C151#12312yes—
111C22×C151C22×D411yescharacteristic
112C2×D151—22no—
113C2×D151—22no—
114C2×D151—22no—
115C2×D151—42no—
116C2×D151—42no—
117C2×D151—42no—
118C2×D151—84no—
119C4×C151—41no—
120C4×C151—41no—
121C4×C151—41no—
122C4×C151—41no—
123C4×C151#12312yes—
124C4×C151C2×#4111yescharacteristic
125C4×C151C2×#4111yescharacteristic
126Dic151—22no—
127Dic151—42no—
128C2×C151—22no—
129C2×C151C2×#12311yescharacteristic
130C2×C151#57611yescharacteristic
131C2×C151#57711yescharacteristic
132D151—42no—
133D151—82no—
134C151#309611yescharacteristic, complemented, Sylow
135#3096—1511nomaximal, Sylow
136#535—1511no—
137#520—1511no—
138#482—1512no—
139#482—1512no—
140#481—1512no—
141#480—1512no—
142#428—1511no—
143#427D15111yescharacteristic, complemented
144#418—1511no—
145C2×#102—1511no—
146#408—1511no—
147C2×#41—1511no—
148C22×D4—1511no—
149C2×M16—1511no—
150C22×C8C2×D15111yescharacteristic
151#127—3021no—
152#124—3021no—
153#121—1512no—
154#121—1512no—
155#120—3022no—
156C4×Q8—3021no—
157C4×D4—3021no—
158C4×D4—3022no—
159#117—1512no—
160#117C2×D15111yescharacteristic
161#117C2×D15111yescharacteristic
162C2×C4⋊C4—1511no—
163C2×C4⋊C4—1512no—
164#107—1512no—
165#107C2×D15111yescharacteristic, complemented
166#107C2×D15111yescharacteristic, complemented
167#106—1512no—
168#106C2×D15111yescharacteristic, complemented
169#106C2×D15111yescharacteristic, complemented
170#102—1512no—
171#102—1512no—
172#102—1512no—
173#102—1512no—
174C22⋊C8—1512no—
175C22⋊C8—1512no—
176C24—3021no—
177#41—3022no—
178#41—3022no—
179C2×Q8—1511no—
180C2×D4—3022no—
181C2×D4—3022no—
182C2×D4—3021no—
183C2×D4—3022no—
184C2×D4—3022no—
185C2×D4—1512no—
186C2×D4—1511no—
187C2×D4—1512no—
188C22×C4—3022no—
189C22×C4—3021no—
190C22×C4—1512no—
191C22×C4C22×D15111yescharacteristic
192M16—3022no—
193C2×C8—22no—
194C2×C8—1512no—
195C2×C8C22×D15111yescharacteristic
196C2×C8C22×D15111yescharacteristic
197C4⋊C4—3022no—
198C4⋊C4—3021no—
199C4⋊C4—1512no—
200C4⋊C4C22×D15111yescharacteristic
201C4⋊C4C22×D15111yescharacteristic
202C4⋊C4C22×D15111yescharacteristic
203C4⋊C4C22×D15111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—21no—
206C22⋊C4—3022no—
207C22⋊C4—3022no—
208C22⋊C4—3022no—
209C42—21no—
210C42—21no—
211C42—3022no—
212C23—3022no—
213C23—6042no—
214C23—1512no—
215C23—12081no—
216C23—12081no—
217C23D4×D15111yescharacteristic
218Q8—3022no—
219D4—3024no—
220D4—3022no—
221D4—3022no—
222D4—3022no—
223D4—6042no—
224D4—12082no—
225D4—12082no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—3022no—
231C2×C4—3022no—
232C2×C4—3022no—
233C2×C4—1512no—
234C2×C4—12082no—
235C2×C4—12081no—
236C2×C4D4×D15111yescharacteristic
237C2×C4#1455900412yes—
238C2×C4#1455900512yes—
239C2×C4C23×D15111yescharacteristic
240C8—21no—
241C8—21no—
242C8—3022no—
243C22—21no—
244C22—21no—
245C22—3022no—
246C22—3022no—
247C22—3022no—
248C22—6042no—
249C22—6042no—
250C22—6042no—
251C22—12084no—
252C22#1801272412yes—
253C22C2×D4×D15111yescharacteristic
254C4—41no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—3022no—
259C4—6042no—
260C4#1801272412yes—
261C4C2×#1455900411yescharacteristic
262C4C2×#1455900511yescharacteristic
263C2—22no—
264C2—6042no—
265C2—12082no—
266C2C2×#1801272411yescharacteristic
267C2#2375301411yescharacteristic
268C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#427×C151C2
socleC22×C151C22×D4
prime radical#23752781C2
hypercenter#427D151
hypocenterC151#3096
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23752692C2semidirect
3. #23752539C2semidirect
4. #23752538C2semidirect
5. #23752532C2semidirect
6. #23752527C2semidirect
7. #23752255C2semidirect
8. #23752216C2semidirect
9. C2×#18012661C2semidirect
10. #23752178C2semidirect
11. #427×C151C2semidirect
23. #18012697C22semidirect
25. C4⋊C4×D151C22semidirect
26. #18012672C22semidirect
27. #18012670C22semidirect
32. (C2×D151)⋊C8C22semidirect
33. (C2×D151)⋊C8C22semidirect
37. #107×C151C22semidirect
38. #107×C151C22semidirect
39. #106×C151C22semidirect
40. #106×C151C22semidirect
134. C151#3096semidirect
143. #427D151semidirect
165. #107C2×D151semidirect
166. #107C2×D151semidirect
168. #106C2×D151semidirect
169. #106C2×D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237527812
#237526922
#237525392
#237525382
#237525322
#237525272
#237522552
#237522162
C2×#180126612
#237521782
#427×C1512
#3096151